Understand
We investigate stabilizer codes with carrier qudits of equal dimension $D$, an arbitrary integer greater than 1.
- We prove that there is a direct relation between the dimension of a qudit stabilizer code and the size of its corresponding stabilizer, and this implies that the code and its stabilizer are dual to each other.
- We also show that any qudit stabilizer can be put in a standard, or canonical, form using a series of Clifford gates, and we provide an explicit efficient algorithm for doing this.
- Our work generalizes known results that were valid only for prime dimensional systems and may be useful in constructing efficient encoding/decoding quantum circuits for qudit stabilizer codes and better qudit quantum error correcting codes.